The objective here is to calculate what value of x for which that statement is true. X itself is just a variable which cab take on any value we need it to but may not necessarily result in the right answer. Case in point, let's pick a value at random: 20.
If X were 20 then...
The first thing you should do is to solve for sinx:
sinx = sqrt(2)/2
Now, to solve x, I am sorry to have to tell you that without a calculator, the only real way to solve this is by knowing the unit circle and its values. In this case x would have to equal 45 degrees,...
The first step is to use trigonometric identities to simplify this expression. One of the most basic trig identities you will ever need to memorize is:
sin^2x + cos^2x = 1
Now, we can manipulate this to find a way to simplify cot^2x by dividing both sides by sin^2x to get this:
Any time you encounter absolute values, that is short hand for saying you have a piece-wise function, or two functions put together. In essence, the function you've been given is shorthand for:
f(x) = -(x+1) = -x-1 for x+1<0 --> x<-1
This is an algebra problem. To set it up, first analyze the numbers and try to create a diagram of the situation.
Let's first label the length L, and width W. It says that the length is 6 [feet] more than twice the width, which allows you to set up this equation:
L = 2W + 6